The linear discriminant function is widely used in epidemiology and disease control studies to estimate the risk of having a disease, and to classify individuals into one of two or more groups. Recently, the robustness of linear discrimination procedures has been studied. That is, how well do these procedures work if the assumptions underlying their use are violated? Procedures other than the linear discriminant function include the quadratic discriminant function and the multiple discriminant function. This study proposes to investigate the robustness of the quadratic and multiple discriminant functions, continue work on the linear discriminant function, determine the effects on risk estimates when assumptions are violated, and to suggest modifications which will improve performance under adverse conditions. Because the mathematical formulation of these problems is extremely complicated, extensive sampling studies will be performed.